Mathematical Sciences: Time Series, Extreme Values and Stochastic Models

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The principal investigators will work in the area of time series analysis and stochastic modeling. The work is divided into two parts. The first part is concerned with problems of estimation and prediction for time series models whose theory is not yet fully understood. These include non-linear, heavy tailed and non-Gaussian processes, all of which play a role in the modelling of real time series data. Efficient estimation and prediction procedures for such series will be sought and their properties will be investigated. Some relatively unexplored models will be considered and some new techniques for state-space modelling of multivariate time series will be investigated. The second part deals with extreme value theory, particularly the interplay between extreme value methods, point processes, asymptotic theory and the application of these ideas to linear, bilinear and general stationary processes.